Personalized Tag Recommendation (PTR) aims to automatically generate a list of tags for users to annotate web resources, the so-called items, according to users’ tagging preferences. The main challenge of PTR is to learn representations of involved entities (i.e., users, items, and tags) from interaction data without loss of structural properties in original data. To this end, various PTR models have been developed to conduct representation learning by embedding historical tagging information into low-dimensional Euclidean space. Although such methods are effective to some extent, their ability to model hierarchy, which lies in the core of tagging information structures, is restricted by Euclidean space’s polynomial expansion property. Since hyperbolic space has recently shown its competitive capability to learn hierarchical data with lower distortion than Euclidean space, we propose a novel PTR model that operates on hyperbolic space, namely HPTR. HPTR learns the representations of entities by modeling their interactive relationships in hyperbolic space and utilizes hyperbolic distance to measure semantic relevance between entities. Specially, we adopt tangent space optimization to update model parameters. Extensive experiments on real-world datasets have shown the superiority of HPTR over state-of-the-art baselines.